It's perfectly possible to be socially functional and adept, even more than just socially functional, but socially 'proficient', and still have social anxiety.
Yeah...get a book on Cognitive Behavioral Therapy like
this one. Also look into meditation, perhaps. These things require work and time, though, and if you need more immediate relief in the short term, look into medication. But they do work - CBT has been found to be as effective as medication (that is, very effective).
But, I'd recommend also you see a therapist or psychiatrist (preferably). If it's at this point where it's very materially affecting your quality of life, basically crippling you like this, then it is time to see someone. The chances are there is NO underlying psychiatric disorder, social anxiety is NOT a disorder in that sense, but it can help to have someone with a psychiatric background to talk to. And they can prescribe medicine if they think you need it. But do be careful about going on something like Xanax - it's very powerful and also addictive in the long term. Talk to a psychiatrist about options...Xanax might be right for you, or maybe something less powerful (like another Valium variant), or maybe something like Prozac which has an anti-anxiety profile, but which isn't addictive.
Oh, by the way, you should go to your GP first. Don't be afraid to open up completely there. He/She will give you a referral to a psychiatrist, and may also get your started on some medicine to tide you over until you see the psychiatrist.
Also, talk to people about this who are close to you. Talking helps enormously with your mental health, whatever the problem. Oh, and realize that this isn't as uncommon as you might think.